I. Introduction to the Population-Sample Decomposition Approach.- I.1 The linear statistical model.- I.2 Minimum distance parameters subject to minimal model assumptions.- II. The Estimation of Linear Relations; The Sample Part of PSD.- II.1 Method of moments and asymptotic distribution theory.- II.2 Asymptotic estimation of covariance functions.- III. Principal Relations.- III.1 Basic formulation of the principal relations.- III.2 The distance matrix Q.- III.3 Simultaneous equations systems.- III.4 Seemingly unrelated regressions.- III.5 Restricted seemingly unrelated regressions.- III.6 Canonical correlation analysis.- IV. Principal Factors.- IV.1 Basic formulation of principal factors.- IV.2 Principal relations versus principal factors.- IV. 3 Principal components analysis.- V. Goodness-of-Fit Measures.- V. 1 Coefficients of multiple correlation and angles between random vectors.- V.2 Coefficients of linear association for principal relations and principal factors.- V.3 Coefficients of linear association for simultaneous equations systems.- V.4 Coefficients of linear association for seemingly unrelated regressions.- VI. Review.- VI.1 A schematic representation of the parameters.- VI.2 List of notation and summary of results.- VII. Computational Aspects of the Population-Sample Decomposition.- VII.1 Fourth-order central moments.- VII.2 Pre- and post-multiplication of V by the gradient matrix.- VII.3 The PSD method in practice.- Preliminaries on matrix algebra.- References.- Author Index.